Briton Naomi Broady claimed a career-best win with victory over Jarmila Gajdosova in Washington DC on Tuesday.
Second seed Kei Nishikori came from a set down to beat Australia's James Duckworth at the Citi Open on Tuesday.
Kimiko Date-Krumm, now 44, fought back from a set down to beat Sabine Lisicki in Stanford on Tuesday.
Sixth seed Philipp Kohlschreiber moved into the second round in Kitzbuhel with victory over Jan-Lennard Struff.
Heather Watson made an early exit from the Citi Open in Washington as she crashed to a first-round defeat.
Two-time champion Robin Haase advanced from the first round at the Generali Open in Kitzbuhel, Austria.
With the fixtures now out, our Andy Schooler looks ahead to the 2015 International Premier Tennis League season.
Andy Murray looks a standout bet at 13/8 to win the Citi Open as the American hard-court swing begins in earnest this week.
John Isner served his way to a third straight BB&T Atlanta Open after crushing Marcos Baghdatis in the final.
Rafael Nadal beat Fabio Fognini in straight sets to win his 47th clay-court title in the bet-at-home Open.